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Engaging students in dynamic and collaborative statistics

Barb Wallis for workshop resourcesbwallis@masseyhigh.school.nzA workshop of activities and ideas, for a differentiated teaching approach, that develops the statistical confidence of Year 9 students in multi-level classrooms.A progression of understanding for students that allows for a movement from counting aspects of discrete data to full appreciation of the inquiry cycle and the descriptive - interpretative aspects within it.

WORKSHOP DO NOW:Fold the paper into eighths 8 pieces, halves, quarters then eighths. Write the number 1 to 8 in the top left corner going across 1 then 2 etc.Write answers to the survey questions[Done with students as the first Yr 9 introduction of the PPDAC cycle whole class, groups, individual assignment]Survey questionsHow did you travel here this morningWhat colour eyes do you have - choose from blue, brown, hazel, greyHow many motor vehicles do you have at your home include motorbikesWhat ethnic group do you identify with most stronglyWhat is the length of your hand-span to the nearest centimetre What time did you get up this morningIn what area is your school located (what was your Year 8 school for students)How many people slept at your house last night

INTRODUCTION:Background referring to the ideas and thinking behind my Maths & Stats teaching and where they have arisen from.

Pip Arnold Multiple aspects of the PPDAC statistical inquiry cyclePeter Hughes Mathematics Pedagogical Content knowledgeCaroline Yoon Model Elicitating ActivitiesJo Boaler How to learn Math


Teaching as a wide NET of ideas and approachesMaths learnt as a whole process and emphasis on relating/understandingInquiry relationship with mathsStatistics alive for themCommunication and collaborationYr 9 scheme progression/expectationsStudent engagementLow entry high ceiling

8Jo Boaler believes by encouraging inquiry, curiosity, confidence & intuition students will develop an inquiry relationship with maths. I think that in our statistics lessons we have an opportunity to act towards this goal.

The world our students will work in relies on teams of people developing ideas, communication and collaboration. As a Maths teacher we can offer them that experience.

Yr 9 MAIN ACTVITIESClass survey questionsInvestigate the throwing of a paper dartRuler drop reactionsFoot sole comparisonC@S Data cards investigations Helicopter rotor blade lengthBig Foot

Getting started: Stats 1Data collection for a Year 9 class. 8 Survey questionsPPDAC cycle ---whole class for one survey question then groups for rest---- draft, feedback, posters --- individual assignments using new data following marking schelude.Collect up data redistribute and follow PPDAC cycle to make a poster. MW & WL PPDAC cycle, posters.Student engagement Stats 1Investigate the throwing of a paper dartPPDAC cycle process complete, relaxed overviewUse of a summative question.

Refer separate sheet. Based on Harrier dart from Peter Newell workshop AMA Sat morning

Low entry high ceilingCheck out our mind-set about ourselves as teachers. We can ask ourselves when looking at a problem, situation or an investigation - ask who is doing the maths? Our classrooms need to be places where people actually do Maths. Problem solve, plan, find the question to ask, explore, give it a go, get it wrong, alter, decide what knowledge is needed, what method would be useful, discuss ideas with each other, explain their methods, hear other ideas and methods. Just as in music if we practice writing the notes and never play or hear an instrument, where is the joy and wonder in that?Stats 1:Ruler drop reaction timesCan take an activity and put the life back in.Can choose parts to structure. Some instructions for data collection are given. Work is done in pairs.Article as conclusion for extension

Refer separate sheet

Stats 3: Comparing and Relationship questionsComparing the foot-length of boys & girlsWorked through with the students providing a structured model over 5 to 8 periods. Diving off into particular areas such as Question types, sources of variation, data of interest, cleaning the data , dot plots to box & whisker graphs, graph shape and descriptions, statistical measures, intervals for histograms etc.Provision of a complete model of the investigation.Census in schools data cardsExplore own question. Quick process teacher provided graphs for question on relationship between popiteal length and height. Students add own data.

Helicopter rotor blade lengthThe structured worksheet is adapted to a PPDAC investigation in a similar way to the paper dart and reaction time by ruler activities. It is a more advanced use of the PPDAC cycle, sources of variation sorted in planning, expanded to whole class data collection and leads to source of box & whisker plots -including graphics calculators if available - use of statistical measures for I notice and conclusions.Also can be used as a basis of discussion of sample results; same scale boxes placed on the wall & then can look at the median variation by forming lines as a border (also upper and lower quartiles). Compare to combining the samples for stats information.Big FootIs an example of a model elicitating activity; Involves a warm-up activity, then a situation that teams work together on to develop an appropriate model that can be used beyond the current situation. In a class where this was used, a girl organised the rest of her group to stand against the wall apart, in proportion to their foot length. A cut-out of the footprint was placed in the best fit place of foot size. The top of the heads were marked as a line and then measured to find height of the person for the police. The model was then written up as a method and developed with the help of the teacher into a scatter graph form, using measurements rather than actual people.RESOURCES Helicopter investigationAlan Santos/Gillian Frankcom Big FootCaroline YoonPPDAC power points and model of foot length investigationAnnie Matthews, Roopa Ashok, Barb Wallis & Nik Wallis Peer assessmentJulie StewartDirty dataPip ArnoldBlack sticks investigationJen TriggsDot plots and Box & Whisker graphsSt Marys Freemans BayMarking scheludes Stats 1 & 3Julie Stewart, Barb Wallis, Robin Knox & Sowbhagya Gundugollu

EXIT CARD[CARD example such as write on the axes what these graphs could be showing collect in to check understanding individual/class]

Workshop = write one workshop idea you are going to enact.